Related papers: Convergence rate in the splitting-up method for ro…
Here, we consider periodic homogenization for time-fractional Hamilton--Jacobi equations. By using the perturbed test function method, we establish the convergence, and give estimates on a rate of convergence. A main difficulty is the…
In this paper, we derive a strong convergence rate of spatial finite difference approximations for both focusing and defocusing stochastic cubic Schr\"odinger equations driven by a multiplicative $Q$-Wiener process. Beyond the uniform…
For a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H> \frac12$ it is known that the classical Euler scheme has the rate of convergence $2H-1$. In this paper we introduce a new numerical…
We approximate the solution $u$ of the Cauchy problem $$ \frac{\partial}{\partial t} u(t,x)=Lu(t,x)+f(t,x), \quad (t,x)\in(0,T]\times\bR^d, $$ $$ u(0,x)=u_0(x),\quad x\in\bR^d $$ by splitting the equation into the system $$…
This paper is concerned with the numerical analysis of the explicit upwind finite volume scheme for numerically solving continuity equations. We are interested in the case where the advecting velocity field has spatial Sobolev regularity…
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class…
We derive a robust error estimate for a recently proposed numerical method for $\alpha$-dissipative solutions of the Hunter-Saxton equation, where $\alpha \in [0, 1]$. In particular, if the following two conditions hold: i) there exist a…
We propose a new explicit numerical scheme for stochastic differential equation with super-linearly growing drift and linearly growing diffusion coefficients which are also twice continuously differentiable. The rate of strong convergence…
The purpose of this paper is concerned with the approximate solution of split equality problems. We introduce two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms. The corresponding strong…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
This paper considers constrained linear dynamic games with quadratic objective functions, which can be cast as affine variational inequalities. By leveraging the problem structure, we apply the Douglas-Rachford splitting, which generates a…
We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse…
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the…
The dynamic iteration method with a restricted additive Schwarz splitting is investigated to co-simulate linear differential algebraic equations system coming from RLC electrical circuit with linear components. We show the pure linear…
In this paper we analyze the convergence of the splitting method for shallow water equations. In particular, we give an analytical estimation of the time step which is necessary for the convergence and then we study the behaviour of the…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…